Structural, electronic, elastic and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys based on rare earth element have been investigated using full-potential linear muffin-tin orbital (FP-LMTO) method within generalized gradient approximation (GGA) in the frame of density functional theory (DFT). By using total energy variations, the independent elastic constants and their pressure dependence have been determined. Also, anisotropic parameter (A), shear modulus (G), Young modulus (E), Poisson’s ratio (ν), ratio (B/G) are calculated. Using quasi-harmonic Debye model, thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys are investigated in temperature range 0–1200 K and pressure range 0–50 GPa. The temperature and pressure effects on the unit cell volume, bulk modulus (B), heat capacities (Cv) at stable volume, (Cp), Debye temperatures (θD), Gibbs energies (G), thermal expansion coefficients (α) and entropies (S) are determined from non-equilibrium Gibbs functions. This study allows to understand deeply the structural and thermodynamic properties of Ni2LaZ (Z = As, Sb and Bi) Heusler alloys in shortest time and cost-effective.